I need help to find out, how Dictionary app showing following popup dialog for selected text on pressing CMD+CTRL+D on any application. I want to implement the same kind of
What you're looking for is a Service. With services, your app doesn't even have to be running or capture global hotkeys.
For example, the functionality of the dictionary app you described is actually a service, observable in the Services menu.

Apple's Service Implementation Guide is probably the best info on services out there.